Transmission of AC power to a remote load is normally assumed to supply an AC waveform in which the current and voltage are in phase for greatest power transfer. This is not the usual case, however, and the loads presented by residential and commercial loads generally provide a reactive and non-linear load, typically inductive, to the power line, resulting in a difference in the phase of voltage and current, normally expressed as a difference angle θ (hereinafter referred to as “phase angle”). There may also be a high harmonic content and additional voltage spikes, both of which affect the connected equipment.
Since this non-zero phase angle supply requires a higher current for the same wattage a non-zero phase angle, or non-unity power factor (cos θ), forces the use of supply lines with greater current capacity, which cost more to provide. To help in correcting a non-zero phase angle power companies normally provide power factor correction at distribution points on the network by means such as synchronous condensers. Despite this the load at each consumer still normally presents an inductive load which is not fully compensated resulting in a non-unity power factor and reduced efficiency in the power distribution system and in the use of the power at the consumer premises. Many electricity suppliers base their charges on the component of power used at zero phase angle or penalise power factors greater than a certain value, such as 0.9, in an effort to encourage greater efficiency by consumers.
Various methods of providing correction at consumer premises have been proposed, such as capacitor banks floated across the consumer line. Such capacitors are normally selected based on the expected load or the prevailing power factor and are not variable. Additionally these methods are expensive to implement and do not necessarily provide a consistent unity power factor.
U.S. Pat. No. 5,355,076 to Chadwick describes one such method in which capacitances are connected in series with a load for at least part of a cycle of the supplied AC waveform.
Therefore a need exists for a solution to the problem of providing a relatively cheap and efficient method of creating an AC supply waveform with unity power factor from an AC supply with non-unity power factor.
The present invention provides a solution to this and other problems which offers advantages over the prior art or which will at least provide the public with a useful choice.
Theory of Operation for Switching Technique:
The term “impedance matching” here means making the non-linear load on the mains line appear to the mains source as a linear load of pure resistance.
It is possible to provide power factor correction by dynamically synthesizing RC networks across the user load which are mostly non-linear in nature. The switching network models and presents the load as linear element to the power source. This reduces the eddy current and I2R losses which in turn leads to efficient power transfer and energy savings.
Consider an AC voltage source,V=Vm Sin 2πft  (1)
Where Vm is the peak voltage and f is the power supply frequency. The corresponding AC current flowing through a load of fixed resistor R is given by,
                    i        =                                            v              m                        R                    ⁢          Sin          ⁢                                          ⁢          2          ⁢                                          ⁢          π          ⁢                                          ⁢          ft                                    (        2        )            
If the fixed resistor R is switched with a time period T the load is synthesized as different resistor R′ whose value depends on the duty cycle in the following manner.
The synthesizing of a resistor R′ from a resistor R where the resistor is switched into a circuit for a time Ton is:
                              R          ′                =                              (                                                            T                  on                                +                                  T                  off                                                            T                on                                      )                    ⁢          R                                    (        3        )            
Where Ton is the on time and Toff is the off time. The term under the bracket represents the duty cycle. The current flow through this synthesized resistor is given by,
                              i          R                =                                            v              m                        R                    ⁢                      (                                          T                on                                                              T                  on                                +                                  T                  off                                                      )                    ⁢          Sin          ⁢                                          ⁢          2          ⁢                                          ⁢          π          ⁢                                          ⁢          ft                                    (        4        )            
Now consider the case of capacitive loads,
A.C. Current flowing through a capacitor C connected to the source voltage V is given by,
                    i        =                              C            ⁢                                          ⅆ                v                                            ⅆ                t                                      ⁢                                                  ⁢                          i              .              e              .                                                          ⁢              i                                =                      2            ⁢                                                  ⁢            π            ⁢                                                  ⁢                          fCV              m                        ⁢            cos            ⁢                                                  ⁢            2            ⁢                                                  ⁢            π            ⁢                                                  ⁢            ft                                              (        5        )            
Similarly, if the capacitor is switched into circuit for part of the time the load is represent as a different value C′ given by
                              C          ′                =                              (                                                            T                  on                                +                                  T                  off                                                            T                on                                      )                    ⁢          C                                    (        6        )            
The current through this synthesized capacitor is given by,i−2πfC′Vm cos 2πft  (7)
Substituting the value of C′ in terms of the capacitor C the load current is given by,
                              i          c                =                  2          ⁢                                          ⁢          π          ⁢                                          ⁢                                    fCV              m                        ⁡                          (                                                T                  on                                                                      T                    on                                    +                                      T                    off                                                              )                                ⁢          Cos          ⁢                                          ⁢          2          ⁢                                          ⁢          π          ⁢                                          ⁢          ft                                    (        8        )            
The following values of the synthesized resistors and capacitors at different duty cycles have been obtained. The fixed values of resistance and capacitor were R=9.1 kΩ and C=91 μF. This combination has a time period RC of 0.828 sec. Table 1 given below shows that keeping the time period fixed at 10 ms (switching frequency 10 kHz) and varying the Ton and Toff maintains the time constant RC to the original value.
TABLE 1Ton (ms)Toff (ms)R′ (KΩ)C′ (μF)R′C′ (sec)9110.181.90.8278211.372.80.8227312.963.70.8216415.154.60.8245518.245.50.8284622.736.40.8263730.327.30.8272845.518.20.8281991.09.10.828
The results emphasize that the product of the switched resistor R and the switched capacitor C (RC) should be constant. The technique can be applied to fixed value of Ton and Toff for a given switching frequency and different values of R and C with the condition that RC remains constant. For practical implementation the value of R and C is selected such that C=2n (where n=0, 1, 2, 3 . . . ). By using an 8 bit binary data 8 different capacitors ranging from 1 μF, 2 μF, 4 μF . . . 256 μF can be switched to get different conditions based on the load.
Electrical Power Equation for Switching Technique:
Where the parallel combination of a switched resistor R and a switched capacitor C is placed across a non-linear load with an AC voltage V applied to it the total power P consumed is given by, P=V.i. cos Φ cost where Φ is the phase angle between voltage V and the load current i.
The total current It is given byit=iR+iC+iL 
Thus the total power is given byP=[V(iR+iC)+ViL] cos Φ  (9)
Substituting the values of iR and iC from equations (4) and (8)
  P  =                         {                              V            ⁡                          [                                                                                          V                      m                                        R                                    ⁢                                      (                                                                  T                        on                                                                                              T                          on                                                +                                                  T                          off                                                                                      )                                    ⁢                  Sin                  ⁢                                                                          ⁢                  2                  ⁢                                                                          ⁢                  π                  ⁢                                                                          ⁢                  ft                                +                                  2                  ⁢                                                                          ⁢                  π                  ⁢                                                                          ⁢                                                            fCV                      m                                        ⁡                                          (                                                                        T                          on                                                                                                      T                            on                                                    +                                                      T                            off                                                                                              )                                                        ⁢                  Cos                  ⁢                                                                          ⁢                  2                  ⁢                                                                          ⁢                  π                  ⁢                                                                          ⁢                  ft                                            ]                                +                      Vi            L                          }            ⁢      Cos      ⁢                          ⁢      ϕ      
The peak voltage Vm, and r.m.s voltage V are related by Vm=√{square root over (2)}V where the applied voltage is a sine voltage. The above given equation can be written as,
                    P        =                              {                                                            2                                ⁢                                                                            V                      2                                        ⁡                                          (                                                                        T                          on                                                                                                      T                            on                                                    +                                                      T                            off                                                                                              )                                                        ⁡                                      [                                                                                            Sin                          ⁢                                                                                                          ⁢                          2                          ⁢                                                                                                          ⁢                          π                          ⁢                                                                                                          ⁢                          ft                                                R                                            +                                              2                        ⁢                                                                                                  ⁢                        π                        ⁢                                                                                                  ⁢                        fC                        ⁢                                                                                                  ⁢                        Cos                        ⁢                                                                                                  ⁢                        2                        ⁢                                                                                                  ⁢                        π                        ⁢                                                                                                  ⁢                        ft                                                              ]                                                              +                              Vi                L                                      }                    ⁢          Cos          ⁢                                          ⁢          ϕ                                    (        10        )            
The power equation contains the terms Ton, Toff, R and C which can be controlled to optimize the value of electrical power transfer to the user load by “impedance matching” the source and load impedances.
All references, including any patents or patent applications cited in this specification are hereby incorporated by reference. No admission is made that any reference constitutes prior art. The discussion of the references states what their authors assert, and the applicants reserve the right to challenge the accuracy and pertinency of the cited documents. It will be clearly understood that, although a number of prior art publications are referred to herein, this reference does not constitute an admission that any of these documents form part of the common general knowledge in the art, in New Zealand or in any other country.
It is acknowledged that the term ‘comprise’ may, under varying jurisdictions, be attributed with either an exclusive or an inclusive meaning. For the purpose of this specification, and unless otherwise noted, the term ‘comprise’ shall have an inclusive meaning—i.e. that it will be taken to mean an inclusion of not only the listed components it directly references, but also other non-specified components or elements. This rationale will also be used when the term ‘comprised’ or ‘comprising’ is used in relation to one or more steps in a method or process.